Branched Integrals

Calculus Level 2

\[\Huge \int_{\int_{2\int_{3\int_{4}^{3} \frac{x}{3} \ dx}^{2}\frac{x}{2} \ dx}^{1}x \ dx}^{\int_{1}^{2\int_{2}^{3\int_{3}^{4} 3x \ dx} 2x \ dx} x \ dx} 1 \ dx\]

If the integral above can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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